# LSAT Logic Games : Solving four- and five-variable logic games

## Example Questions

### Example Question #31 : Solving Four And Five Variable Logic Games

Four baseball players are the leaders in five statistical categories.  Each player is the leader in at least one category.  The players are Howard, Jennings, Robinson, and Sanchez.  The categories are home runs (HR), runs batted in (RBI), runs scored (R), doubles (2B), and stolen bases (SB).  You are aware of the following facts regarding the players' statistics:

Howard hit more home runs than Robinson.

Sanchez had more runs scored than Howard.

Jennings finished last in the categories of home runs and runs batted in.

Robinson had twice as many stolen bases as Jennings.

Sanchez hit more doubles than Robinson and Howard.

In which category could any player potentially be the leader?

None of the categories

Doubles

Stolen Bases

Runs Batted In

Runs

None of the categories

Explanation:

There is no category in which any player could potentially be the leader.  There is at least one player who could not be the leader in each category to choose from, as well as in home runs.

### Example Question #31 : Solving Four And Five Variable Logic Games

Four baseball players are the leaders in five statistical categories.  Each player is the leader in at least one category.  The players are Howard, Jennings, Robinson, and Sanchez.  The categories are home runs (HR), runs batted in (RBI), runs scored (R), doubles (2B), and stolen bases (SB).  You are aware of the following facts regarding the players' statistics:

Howard hit more home runs than Robinson.

Sanchez had more runs scored than Howard.

Jennings finished last in the categories of home runs and runs batted in.

Robinson had twice as many stolen bases as Jennings.

Sanchez hit more doubles than Robinson and Howard.

Which of the following could be a correct representation of the leaders in each statistical category?

Howard in HR; Sanchez in RBI; Jennings in R and 2B; Robinson in SB.

Robinson in HR; Sanchez in R and RBI; Jennings in 2B; Howard in SB.

Sanchez in HR and R; Jennings in RBI; Howard in 2B; Robinson in SB.

Howard in HR and R; Sanchez in RBI; Jennings in 2B; Robinson in SB.

Sanchez in HR and RBI; Jennings in R; Robinson in 2B; Howard in SB.

Howard in HR; Sanchez in RBI; Jennings in R and 2B; Robinson in SB.

Explanation:

The correct answer is: Howard in HR; Sanchez in RBI; Jennings in R and 2B; Robinson in SB.  All the other choices would not correspond with one of the listed facts.

### Example Question #31 : Solving Four And Five Variable Logic Games

Four baseball players are the leaders in five statistical categories.  Each player is the leader in at least one category.  The players are Howard, Jennings, Robinson, and Sanchez.  The categories are home runs (HR), runs batted in (RBI), runs scored (R), doubles (2B), and stolen bases (SB).  You are aware of the following facts regarding the players' statistics:

Howard hit more home runs than Robinson.

Sanchez had more runs scored than Howard.

Jennings finished last in the categories of home runs and runs batted in.

Robinson had twice as many stolen bases as Jennings.

Sanchez hit more doubles than Robinson and Howard.

Which one of the following could NOT be a correct representation of the leaders in each statistical category?

Howard in HR and RBI; Sanchez in R; Jennings in 2B; Robinson in SB

Sanchez in HR; Robinson in RBI; Jennings in R and 2B; Howard in SB

Sanchez in HR; Robinson in RBI and SB; Jennings in R; Howard in 2B

Sanchez in HR and 2B; Howard in RBI; Jennings in R; Robinson in SB

Howard in HR; Sanchez in R; Robinson in RBI and SB; Jennings in 2B

Sanchez in HR; Robinson in RBI and SB; Jennings in R; Howard in 2B

Explanation:

The correct answer is "Sanchez in HR; Robinson in RBI and SB; Jennings in R; Howard in 2B." The facts indicate that Sanchez had more doubles than Robinson and Howard. Therefore, Howard cannot be the leader in doubles and this answer choice cannot be correct.

### Example Question #31 : Four & Five Variable

Four baseball players are the leaders in five statistical categories.  Each player is the leader in at least one category.  The players are Howard, Jennings, Robinson, and Sanchez.  The categories are home runs (HR), runs batted in (RBI), runs scored (R), doubles (2B), and stolen bases (SB).  You are aware of the following facts regarding the players' statistics:

Howard hit more home runs than Robinson.

Sanchez had more runs scored than Howard.

Jennings finished last in the categories of home runs and runs batted in.

Robinson had twice as many stolen bases as Jennings.

Sanchez hit more doubles than Robinson and Howard.

If Howard was the leader in runs batted in only and Jennings was the leader in runs scored only, which of the following would be true?

None of the other answers; the premise of the question cannot be true

Robinson would be the leader in home runs and stolen bases

Sanchez would be the leader in home runs and stolen bases

Sanchez would be the leader in home runs and doubles

Robinson would be the leader in doubles and stolen bases

Sanchez would be the leader in home runs and doubles

Explanation:

If Howard was the leaders in runs batted in only and Jennings was the leader in runs scored only, then Sanchez would have to be the leader in home runs and doubles. The only other player, Jennings, cannot be the leader in home runs (Howard hit more) or doubles (Sanchez had more). In addition, every player must be the leader in at least one category. Under this scenario, Robinson would be the leader in stolen bases. For those reasons, the premise of the question can be true.

### Example Question #32 : Solving Four And Five Variable Logic Games

Four baseball players are the leaders in five statistical categories.  Each player is the leader in at least one category.  The players are Howard, Jennings, Robinson, and Sanchez.  The categories are home runs (HR), runs batted in (RBI), runs scored (R), doubles (2B), and stolen bases (SB).  You are aware of the following facts regarding the players' statistics:

Howard hit more home runs than Robinson.

Sanchez had more runs scored than Howard.

Jennings finished last in the categories of home runs and runs batted in.

Robinson had twice as many stolen bases as Jennings.

Sanchez hit more doubles than Robinson and Howard.

Of all the potential leaders in each category, which player could be the leader in the fewest categories?

Howard

Robinson

Sanchez

None of the other answers

Jennings

Jennings

Explanation:

Jennings could be the potential leader in the fewest categories. Jennings cannot be the leader in home runs, runs batted in, or stolen bases. Therefore, Jennings can only potentially be the leader in two categories: runs scored and doubles. Howard and Robinson can each potentially be the leader in three categories, while Sanchez can potentially be the leader in any of the five categories.

### Example Question #31 : Solving Four And Five Variable Logic Games

A popular band is preparing for a nationwide music tour.  The tour must include the following five states: California, Florida, Illinois, New York, and Texas.  The tour will conclude in one state before moving to the next state.  The following restrictions apply to the tour dates:

The tour must start in New York or California.

Texas cannot be the final state.

Texas and Illinois must be consecutive, with either coming first.

Florida must be after New York.

New York and California must not be consecutive to each other.

Which of the following could be a proper chronological sequence of states for the tour?

California, New York, Texas, Illinois, Florida

California, Illinois, Texas, New York, Florida

California, Texas, Illinois, Florida, New York

New York, Florida, California, Illinois, Texas

New York, Texas, Florida, Illinois, California

California, Illinois, Texas, New York, Florida

Explanation:

The correct sequence is: California, Illinois, Texas, New York, Florida.  This is the only sequence provided in which the tour starts in New York or California, Texas and Illinois are consecutive, New York and California are not consecutive, Florida is after New York, and Texas is not last.

### Example Question #31 : Solving Four And Five Variable Logic Games

There are five scientists in a laboratory: Abbi, Barry, Carri, Danny, and Evi. Each scientist performs experiments with one of three pieces of equipment: the laser, the test tube, or the microscope. The following conditions must apply:

• Abbi and Barry do not use the same piece of equipment as each other, nor do they use the same piece of equipment as Danny.
• Exactly two scientists use the laser.
• Evi and Danny use different pieces of equipment.
• If either Abbi or Carri use the microscope, they both use the microscope.

Which one of the following could be an accurate list of the pieces of equipment used by the scientists in the following order: Abbi, Barry, Danny, Evi, Carri?

Laser, Test Tube, Microscope, Laser, Laser

Laser, Test Tube, Microscope, Laser, Microscope

Microscope, Test Tube, Laser, Laser, Microscope

Microscope, Laser, Laser, Test Tube, Microscope

Laser, Test Tube, Microscope, Laser, Test Tube

Laser, Test Tube, Microscope, Laser, Test Tube

Explanation:

Abbi, Barry and Danny must use different pieces of equipment; Evi and Danny must use different pieces of equipment; two of our scientists use the laser; and if Abbi or Carri use the microscope, they both must use the microscope. Following these conditions, Abbi uses the laser, which means that Carri cannot use the microscope. Barry uses the test tube and Danny uses the microscope, which finishes off our first condition. Evi uses the laser which satisfies two of our conditions. With Carri using the test tube, that finishes off the correct answer. It is correct because it does not violate any of the conditions where as all of the other answers do violate one or more of the conditions.

### Example Question #33 : Solving Four And Five Variable Logic Games

There are five scientists in a laboratory: Abbi, Barry, Carri, Danny, and Evi. Each scientist performs experiments with one of three pieces of equipment: the laser, the test tube, or the microscope. The following conditions must apply:

• Abbi and Barry do not use the same piece of equipment as each other, nor do they use the same piece of equipment as Danny.
• Exactly two scientists use the laser.
• Evi and Danny use different pieces of equipment.
• If either Abbi or Carri use the microscope, they both use the microscope.

If Carri uses the laser, then which one of the following must be false?

Abbi uses the Test Tube.

Abbi uses the Laser.

Barry uses the Microscope.

Evi uses the Microscope.

Evi uses the Laser.

Evi uses the Laser.

Explanation:

Evi using the laser must be false because, if Carri is using the laser and Abbi, Barry and Danny must use different pieces of equipment, then the two placeholders under laser would be filled by Carri and Evi leaving no room for either Abbi, Barry or Danny. Thus, Abbi, Barry, and Danny will not be able to remain using separate pieces of equipment if Carri uses the laser.

### Example Question #32 : Solving Four And Five Variable Logic Games

There are five scientists in a laboratory: Abbi, Barry, Carri, Danny, and Evi. Each scientist performs experiments with one of three pieces of equipment: the laser, the test tube, or the microscope. The following conditions must apply:

• Abbi and Barry do not use the same piece of equipment as each other, nor do they use the same piece of equipment as Danny.
• Exactly two scientists use the laser.
• Evi and Danny use different pieces of equipment.
• If either Abbi or Carri use the microscope, they both use the microscope.

Which of the following is a pair of scientists who could use the microscope together?

Abbi and Evi

Danny and Barry

Barry and Carri

Barry and Evi

Danny and Evi

Barry and Evi

Explanation:

Two answer combinations, Abbi and Evi, and Barry and Carri, cannot be correct because that leaves one of the placeholders under laser unoccupied. Danny and Evi cannot be correct because of our condition that says Danny and Evi must use different pieces of equipment. Danny and Barry cannot be correct again because a condition explicitly says they must be separate. Finally, through process of elimination, Barry and Evi must be correct.

### Example Question #35 : Solving Four And Five Variable Logic Games

There are five scientists in a laboratory: Abbi, Barry, Carri, Danny, and Evi. Each scientist performs experiments with one of three pieces of equipment: the laser, the test tube, or the microscope. The following conditions must apply:

• Abbi and Barry do not use the same piece of equipment as each other, nor do they use the same piece of equipment as Danny.
• Exactly two scientists use the laser.
• Evi and Danny use different pieces of equipment.
• If either Abbi or Carri use the microscope, they both use the microscope.

Each of the following statements must be false EXCEPT __________.

Only Danny uses the Test Tube

Only Evi uses the Test Tube

Evi and Carri use the Test Tube together

Only Barry uses the Test Tube

Only Carri uses the Test Tube